An apparatus of the generic type known from DE 23 42 444 A1 serves for manufacturing corrugated pipes. To this effect two supply lines are provided in a line conduit of the injection head, which--seen in the direction of production--are bent over at the rear end of the temperature-regulating bell and connected frontally to a coolant flow pipe and a coolant return pipe, respectively, of a cooling channel. This embodiment with two rigid supply pipes is rather inflexible.